Processing geophysical data using 3d norm-zero optimization for smoothing geophysical inversion data

ABSTRACT

The present disclosure describes methods and systems, including computer-implemented methods, computer program products, and computer systems, for processing geophysical data. One computer-implemented method includes obtaining a set of raw geophysical data, wherein the raw geophysical data include 3-Dimensional (3D) coordinates; grouping, by a data processing apparatus, the set of the raw geophysical data into a plurality of subsets; and processing, by the data processing apparatus, each subset of the raw geophysical data using a 3D norm zero objective energy function to generate a subset of smoothed geophysical data, wherein the smoothed geophysical data is used to build a subsurface model.

BACKGROUND

In a geophysics inversion analysis, geophysical data is collected andanalyzed to estimate the subsurface structure of the earth. Examples ofgeophysical data include impedance data, porosity data, and velocitydata. In some cases, the geophysical data can be used to build ageographic model that assists in making drilling decisions.

SUMMARY

The present disclosure describes methods and systems, includingcomputer-implemented methods, computer program products, and computersystems for processing geophysical data. One computer-implemented methodfor processing geophysical data includes obtaining a set of rawgeophysical data, wherein the raw geophysical data include 3-Dimensional(3D) coordinates; grouping, by a data processing apparatus, the set ofthe raw geophysical data into a plurality of subsets; and processing, bythe data processing apparatus, each subset of the raw geophysical datausing a 3D norm zero objective energy function to generate a subset ofsmoothed geophysical data, wherein the smoothed geophysical data is usedto build a subsurface model.

Other implementations of this aspect include corresponding computersystems, apparatuses, and computer programs recorded on one or morecomputer storage devices, each configured to perform the actions of themethods. A system of one or more computers can be configured to performparticular operations or actions by virtue of having software, firmware,hardware, or a combination of software, firmware, or hardware installedon the system that, in operation, causes the system to perform theactions. One or more computer programs can be configured to performparticular operations or actions by virtue of including instructionsthat, when executed by data processing apparatus, cause the apparatus toperform the actions.

The foregoing and other implementations can each optionally include oneor more of the following features, alone or in combination:

A first aspect, combinable with the general implementation, wherein theraw geophysical data is at least one of impedance data, velocity data,or porosity data.

A second aspect, combinable with any of the previous aspects, whereingrouping the set of the raw geophysical data into a plurality of subsetsincludes determining geometry information for the set of the rawgeophysical data; determining a memory size for processing a subset ofthe raw geophysical data by the data processing apparatus; and groupingthe set of the geophysical data based on the geometry information andthe memory size.

A third aspect, combinable with any of the previous aspects, wherein thegeometry information includes a cross line direction of the rawgeophysical data.

A fourth aspect, combinable with any of the previous aspects, whereinthe 3D norm zero objective energy function is obj=Σ_(x=1)^(k)((d(x)−m(x))²+λ·Σ_(i=1) ³C(∂m(x)/∂x_(i)≠0)), where d(x) representsthe subset of the raw geophysical data, k represents the number of theraw geophysical data in the subset, i represents the dimension of theraw geophysical data, m(x) represents the subset of the smoothedgeophysical data, C( . . . ) represents a counting function, andrepresents a constant weight.

A fifth aspect, combinable with any of the previous aspects, whereinprocessing each subset of the raw geophysical data includes iterativelyprocessing until an iterative condition is met, the iterative processingincluding computing an auxiliary value by solving a first sub energyfunction, wherein the first sub energy function is derived from the 3Dnorm zero objective energy function with a fixed value of an input data;computing a next input data by solving a second sub energy function,wherein the second sub energy function is derived from the 3D norm zeroobjective energy function with a fixed auxiliary value; and increasing abeta value that is included in the first and the second sub energyfunctions.

A sixth aspect, combinable with any of the previous aspects, wherein theiteration condition includes at least one of reaching a predeterminednumber of iterations or a beta value being over a predeterminedthreshold.

The subject matter described in this specification can be implemented inparticular implementations so as to realize one or more of the followingadvantages. Using a 3D norm zero optimization process to smooth the rawdata can enhance a seismic inversion image by removing noise andpreserving the edges. This approach can provide a smooth model to betterimage complex geological structures. The resulted data model can helpgeological interpreters to build a more coherent reservoir model,improve drilling location accuracy, and save operational cost. The 3Dnorm zero optimization process described is also computation efficientbecause the solution uses a low term of multiplication and summation.Furthermore, the 3D norm zero function may be used as a global operatorthat may not be affected by local abnormality. In addition, the 3D normzero function may not be limited by window sizes that may be required inalgorithms using median filters. Other advantages will be apparent tothose of ordinary skill in the art.

The details of one or more implementations of the subject matter of thisspecification are set forth in the accompanying drawings and thedescription below. Other features, aspects, and advantages of thesubject matter will become apparent from the description, the drawings,and the claims.

DESCRIPTION OF DRAWINGS

FIG. 1 illustrates an example 3D norm zero optimization method accordingto an implementation.

FIG. 2 is an example Society of Exploration Geophysicists-Y (SEGY) file200 storing the raw geophysical data according to an implementation.

FIG. 3 is a block diagram of an example grouping for a set of rawgeophysical data according to an implementation.

FIG. 4 illustrates an example method of processing a block ofgeophysical data using 3D norm zero function according to animplementation.

FIG. 5 is a high-level architecture block diagram of a geophysical dataprocessing system according to an implementation.

FIGS. 6A & 6B are example screenshots which illustrate velocity dataaccording to an implementation.

FIGS. 7A & 7B are example screenshots which illustrate an inline sectionview of a 3D seismic survey according to an implementation.

FIGS. 8A & 8B are example screenshots which illustrate a 3D volume viewof an acoustic impedance model according to an implementation.

FIGS. 9A & 9B are example screenshots which illustrate a 2D section viewof an acoustic impedance model according to an implementation.

FIGS. 10A & 10B are example screenshots which illustrate a time sliceview of an acoustic impedance model according to an implementation.

FIGS. 11A & 11B are example screenshots which illustrate a porositymodel according to an implementation.

Like reference numbers and designations in the various drawings indicatelike elements.

DETAILED DESCRIPTION

The following description is presented to enable any person skilled inthe art to make and use the disclosed subject matter, and is provided inthe context of one or more particular implementations. Variousmodifications to the disclosed implementations will be readily apparentto those skilled in the art, and the general principles defined hereinmay be applied to other implementations and applications withoutdeparting from scope of the disclosure. Thus, the present disclosure isnot intended to be limited to the described and/or illustratedimplementations, but is to be accorded the widest scope consistent withthe principles and features disclosed herein.

This disclosure generally describes methods and systems, includingcomputer-implemented methods, computer program products, and computersystems, for processing geophysical data. In seismic processing,geophysical data can be used to build geographic models of subsurfacestructures. In some cases, the geophysical data have the features ofsparseness. These geophysical data can also be blocky and have naturaledges. Examples of these geophysical data can include impedance data,porosity data, and velocity data. In these or other cases, the rawgeophysical data can be processed by a computer system to optimize thesmoothness of the data and, therefore, can provide a more accurate imagefor the development of geographic models. For example, velocity data canbe used to determine seismic reflection through depth/time migration.The accuracy of the migration can depend on the accuracy of the velocitymodel, especially in a complex subsalt dome area. A smoothed velocitymodel can improve the migration image, and therefore can be used tobuild a more accurate reservoir model. In some cases, median filter orstructure-oriented filter can be used to filter the raw data. However,these filters may not work well on geophysical data that representblocky layered structure images.

A norm is a total size or length of all vectors in a vector space ormatrices. A n^(th) norm, denoted as l_(n)-norm, is defined as then^(th)-root of a summation of all elements to the n^(th) power. In somecases, l₁-norm is also referred to as Euclidean distance, and l₂-norm isalso referred to as the Mean-squared Error. The following equationrepresents the definition of the l_(n)-norm for a group of vectorsx_(i):

$\begin{matrix}{{x}_{n} = {\sqrt[n]{\sum_{i}{x_{i}}^{n}}\mspace{14mu} {Where}\mspace{14mu} n\; \varepsilon \; {{\mathbb{R}}( {{Real}\mspace{14mu} {number}} )}}} & (1)\end{matrix}$

The following represents a definition of norm-two, denoted as l₂, for aset of numbers that are denoted as x(t):

l ₂=(x(t))²  (2)

The following represents a definition of norm-one, denoted as l₁ forx(t):

l ₁ =Σ∥x(t)∥  (3)

In some cases, a norm zero optimization can be used to find the sparsestsolution of a linear system. The norm zero optimization can also bereferred to as the l₀-norm optimization or the l₀-optimization. A normzero optimization can be applied to geophysical data, e.g., impedance,porosity, or velocity, or any data that presents layer or blockystructure image. Applying a norm zero optimization to geophysical datawith sparseness feature can smooth the data and, therefore, producesbetter geophysical models. In a norm zero optimization, the l₀-norm of avector can be minimized according to some constraints. The followingrepresents an expression of the norm zero optimization problem: min∥x∥₀Subject to Ax=b.

In some cases, norm zero optimization can be used to determine thenumber of interfaces between lithological units based on a group ofmeasured points. Initially, while the number of data points is muchlarger than the number of lithological units, every measured point couldpotentially be a major interface. The optimization procedure reduces thenumber of pseudo lithological interfaces from a large number to asmaller based on a least square error principle. A thicker lithologicallayer could contain hundreds of measured data points. Therefore, normzero optimization can be used to smooth the data points and group theminto segments to match the statistical characters of the layered earthmodel.

While l_(2—)norm is commonly used in the field of engineering andscience, l_(0—)norm is much less applicable. Due to its complexity,l_(0—)norm is often difficult to solve practically. The followingequation represents the definition of the l₀-norm for a group of vectorsx_(i):

$\begin{matrix}{{x}_{0} = \sqrt[0]{\sum_{i}x_{i}^{0}}} & (4)\end{matrix}$

To avoid the presence of zero^(th)-power and zero^(th)-root in the abovedefinition, in some cases, an alternative definition of l₀-norm can beused. In the alternative definition, l_(0—)norm is defined to representa total number of non-zero elements in a vector. The following equationrepresents the alternative definition of the l₀-norm for a vector x:

∥x∥ ₀=≠(i|x _(i)≠0)  (5)

The following represents a definition of norm zero, denoted as l₀:

l ₀ =ΣC(x(t))  (6)

Where the counting function C is represented as the following:

$\begin{matrix}{{C(x)} = \{ \begin{matrix}1 & {x \neq 0} \\0 & {x = 0}\end{matrix} } & (7)\end{matrix}$

Unlike norm two, norm zero is not analytic. Therefore, its derivativecannot be obtained numerically. In some cases, norm zero optimizationcan be used to process 2-dimensional (2D) images. However, forgeophysical data with 3-dimensional (3D) coordinates, a norm zerooptimization for 2D data may not provide consistent images on cross linedirections.

In some cases, a norm zero optimization process for 3D data can be usedto smooth the raw geophysical data. The process can be applied on blockystructured geophysical data as an edge-preserving smoothing filter tobuild a better 3D model for geological interpretation. In some cases, asdiscussed in more detail in FIGS. 1-11 and associated descriptions, thegeophysical data are obtained, segmented, and processed based on a 3Dnorm zero objective energy function. In some cases, the 3D norm zeroobjective energy function is solved by using a two-step iterativeprocess. The two-step iterative process includes fixing an input data tosolve for an auxiliary value, and fixing the auxiliary value to solvefor the next input data. The optimization process enhances imageresolution by removing low amplitude components while preserving sharpedges, thus providing better geological interpretation models. Theoptimization process is computation efficient on improving data quality.

FIG. 1 illustrates an example 3D norm zero optimization method 100according to an implementation. For clarity of presentation, thedescription that follows generally describes method 100 in the contextof FIGS. 2-11. However, it will be understood that method 100 may beperformed, for example, by any other suitable system, environment,software, and hardware, or a combination of systems, environments,software, and hardware as appropriate. In some implementations, varioussteps of method 100 can be run in parallel, in combination, in loops,and/or in any order.

At 102, a set of raw geophysical data is obtained. In some cases, theraw geophysical data are 3D data that include 3D coordinatescorresponding to a (x, y, z) coordinate system. In some cases, the dataare stored in a Society of Exploration Geophysicists (SEG) format, e.g.,the SEG-Y (SEGY) format.

FIG. 2 is an example SEGY file 200 storing the raw geophysical dataaccording to an implementation. The file 200 includes a file header 210and one or more trace files 220 a-b. The file header 210 can include anoptional SEGY tape label, a textual file header, a binary file header,and one or more optional extended textual file headers. In some cases,the raw geophysical data are stored trace by trace. Each trace file,e.g., trace files 220 a-b, can include a trace header 222 and a tracedata 224. In some cases, the trace header 222 has 240 bytes. The traceheader 222 can include the geometry information for the raw geophysicaldata in the trace. Examples of the geometry information include theinline number, the cross line number, sample rate, depth, and recordedtime for the raw geophysical data. The trace data 224 can include theraw geophysical data in the trace.

Referring to FIG. 1, from 102, method 100 proceeds to 104, where thegeometry information of the raw data are determined. The geometryinformation can include the inline number, the cross line number, samplerate, depth, or recorded time for the raw data. In some cases, thegeometry information for the raw data in a trace can be determined basedon a trace header of the trace in the SEGY file. From 104, method 100proceeds to 106.

At 106, a memory size for performing the optimization process isdetermined. In some cases, the memory size includes the size of memorythat the computer system can use to store a block of data, perform thecomputation procedures described in FIGS. 1-11 for the block of data,and output the data to a file. From 106, method 100 proceeds to 108.

At 108, the set of raw data is grouped into one or more blocks. In somecases, the set of raw data can include a large number of data. In theseor other cases, the set of raw data can be grouped into a plurality ofblocks. Each block of raw data can be processed together. This approachenables the optimization process to be performed by a computer systemwith limited memory and processing power. In some cases, the groupingcan be determined based on the geometry information of the raw datadetermined at 104, the memory size for performing the optimizationprocess determined at 106, or a combination of both. For example, asillustrated in FIG. 3, the grouping can be determined based on the crossline directions of the data and the memory size.

FIG. 3 is a block diagram 300 of an example grouping for a set of rawgeophysical data according to an implementation. As illustrated, thedata are organized based on their inline and cross line numbers in arectangle box. The width of the length represents the inline directionsof the data. The length of the box represents the cross line directionsof the data. The data are then grouped into blocks along the cross linedirections. The size of the cross line direction for each block isdetermined based on the memory size for processing the block. In somecases, the raw data does not fit in a regular rectangle box, e.g., somedata are missing in one or more blocks. In these or other cases, the rawdata are regularized. For example, additional data with the value 0 canbe added for each block to make the data in each block form a rectanglebox.

In some cases, edge artifacts may be introduced by the segmentation ofdata into blocks and the processing of individual blocks. To smooth outthese edge artifacts, the output data for each block is generated byprocessing a buffer block of data that includes data from adjacentblocks. In these or other cases, the size of each block is determinedbased on the memory size needed to process the data in a buffer block.For example, as shown in FIG. 3, the set of raw data is grouped into 4blocks, block-1 302, block-2 304, block-3 306, and block-4 308 along thecross line direction. When block-1 302 is processed, the data in bufferblock 1 input 312 is used as input. The buffer block 1 input 312includes data in the block-1 302 and data in the upper portion of theadjacent block-1 304. The optimization process can generate output datain block 1 output 322, which is the same size as the block-1 302. Thedata in buffer block-2 input 314 is used as input to produce output datain block-2 output 324. The buffer block-2 input 314 includes data in theblock-2 304, data in the lower portion of the adjacent block-1 302, anddata in the upper portion of the adjacent block-3 306. Similarly, thedata in buffer block-3 input 316 and buffer block-4 input 318 are usedas inputs to produce output data in block-3 output 326 and block-4output 328, respectively. In some cases, the size of the last block inthe set can be smaller than other blocks.

Referring to FIG. 1, from 108, method 100 proceeds to 110, where eachblock, or a buffer block as discussed above, of raw data is processedbased on a 3D norm zero optimization process. FIG. 4 and associateddescription provides additional details of these implementations. From110, method 100 proceeds to 112.

At 112, the smoothed data for each block is outputted into an outputfile. In some cases, the output data can be stored in a SEGY file. Insome cases, the output data is de-regularized. In a de-regularizationprocess, the size of output data for each block is restored to theoriginal size of the input data. For example, if a number of additionaldata is added to make the data fit into a regular rectangle box in ablock, the same number of output data is removed. The optimization stepat 110 and the output step at 112 are repeated until the last block ofdata in the set is processed.

FIG. 4 illustrates an example method 400 of processing a block ofgeophysical data using 3D norm zero function according to animplementation. For clarity of presentation, the description thatfollows generally describes method 400 in the context of FIGS. 1-3 and5-11. However, it will be understood that method 400 may be performed,for example, by any other suitable system, environment, software, andhardware, or a combination of systems, environments, software, andhardware as appropriate. In some implementations, various steps ofmethod 400 can be run in parallel, in combination, in loops, and/or inany order.

In some cases, the 3D norm zero function can be solved in a two-stepiterative process. The following represents the 3D norm zero objectiveenergy function to be solved:

$\begin{matrix}{{obj} = {\sum_{x = 1}^{k}( {( {{d(x)} - {m(x)}} )^{2} + {\lambda \cdot {\sum_{i = 1}^{3}{C( {\frac{\partial{m(x)}}{\partial x_{i}} \neq 0} )}}}} )}} & (8)\end{matrix}$

where d(x) enumerates k samples of 3D raw data, where xεR³; i enumeratesthe dimension of the raw data; m(x) represents the smooth version of thedata; C( ) represents the l₀ function, which is a counting function thatreturns 0 if the input of the function is zero and returns 1 if theinput of the function is not zero; λ represents a constant weight; and xenumerates all the pixels in the image.

The above function is neither smooth nor continuous and, therefore, notdirectly solvable if by close form or gradient based methods. Toapproximate the solution, an auxiliary variables {h_(i)} is introduced.The following represents a definition of the auxiliary variables{h_(i)}:

$\begin{matrix}{h_{i}->\frac{\partial m}{\partial x_{i}}} & (9)\end{matrix}$

Therefore, the objective energy function can be rewritten in thefollowing:

${obj} = {\sum_{x = 1}^{k}( {( {{d(x)} - {m(x)}} )^{2} + {\beta \cdot {\sum_{i = 1}^{3}( {{h_{i}( x_{i} )} - \frac{\partial{m(x)}}{\partial x_{i}}} )^{2}}} + {\lambda \cdot {\sum_{i = 1}^{3}{C( {{h_{i}(x)} \neq 0} )}}}} )}$

(10)

When the beta value {β} is large enough, the auxiliary variables {h_(i)}approach the derivative of m(x). Thus, the model in the equation (10)approaches equation (8).

It may be difficult to analytically solve equation (10) because the twoterms m(x) and h(x) model respectively the pixel-wise difference andglobal discontinuity statistically and, thus, are not suitable fortraditional gradient descent or other discrete optimization methods. Insome cases, an alternating optimization solution with half-quadraticsplitting can be used. The solution can be performed in a loop of twoalternating steps using an iteration approach: First, fix m and solvefor h; and second, fix h and solve for m. Then, the value of β isincreased before entering the next iteration. The iteration loopcontinues until an iterative condition is met. The followingdescriptions provide additional details of these implementations.

Referring to FIG. 4, at 402, the parameters for the optimization processare initialized. The parameters can include an initial beta value β. Forexample, β can be initialized to 0.5. The parameters can also include acut off ratio β. In some cases, a cut off ratio of 0.5 can create aminor smoothing effect, while a cut off ratio of 0.95 can generateheavily smoothed and blocky data. The parameters can also include theiterative condition. For example, the iterative condition can include amaximum number of iterations, a maximum number of β, a smoothing qualityof the output data, or a combination of both. In some cases, some or allof the parameters can be initialized one time for raw data in differentblocks or different traces; therefore, the same initiation values can beused. Alternatively or additionally, the parameters can be initializedeach time the raw data in different blocks or traces are processed;therefore, different initiation values can be used. In some cases, theinitial value of the output data m(x) can be set to d(x). In these orother cases, the derivative operator ∂m(x)/∂x_(i) is also computed. From402, method 400 proceeds to 404.

At 404 auxiliary variables {h_(i)} is computed. In this step, m isfixed, and h can be solved using a sub energy optimization functiondescribed as the following:

$\begin{matrix} {{\arg \{ \min_{h} \}} = {\sum_{x = 1}^{k}( {{\beta \cdot {\sum_{i = 1}^{3}( {{h_{i}(x)} - \frac{\partial{m(x)}}{\partial x_{i}}} )^{2}}} + {\lambda \cdot {\sum_{i = 1}^{3}{C( {{h_{i}(x)} \neq 0} )}}}} )}} ) & (11)\end{matrix}$

The following represents the solution h:

$\begin{matrix}\{ \begin{matrix}{{h_{i}(x)} = {{\frac{\partial{m(x)}}{\partial x_{i}}\mspace{14mu} {if}\mspace{14mu} \frac{\partial{m(x)}}{\partial x_{i}}} \geq \frac{\lambda}{\beta}}} \\{{h_{i}(x)} = {0\mspace{14mu} {otherwise}}}\end{matrix}  & (12)\end{matrix}$

This step removes small gradients and keeps the larger ones for futureiterations. As illustrated in the equation, the power threshold λ/β cancontrol the sparseness of the rock interfaces. A larger value λ/β canproduce a blockier result. From 406, method 400 proceeds to 408.

In some cases, the constant weight λ can be computed by multiplying thecutoff ratio P and the power of

$\frac{\partial{m(x)}}{\partial x_{i}}.$

The power of

$\frac{\partial{m(x)}}{\partial x_{i\;}}$

can be computed as following:

power of

$\frac{\partial{m(x)}}{\partial x_{i}} = {{\frac{\partial{m(x)}}{\partial x_{1}}*\frac{\partial{m(x)}}{\partial x_{1}}} + {\frac{\partial{m(x)}}{\partial x_{2}}*\frac{\partial{m(x)}}{\partial x_{2}}} + {\frac{\partial{m(x)}}{\partial x_{3}}*\frac{\partial{m(x)}}{\partial x_{3}}}}$where  x 1, x 2, x 3

represents 3D space coordinate directions. From 404, method 400 proceedsto 406.

At 406, 3D discrete Fourier transform of the input data m(x) and theauxiliary variables {h_(i)} are computed. As discussed in more detailbelow, the 3D discrete Fourier transform of the input data and thedirective operators can be used to solve the frequency domain version ofthe function. In some cases, the 3D discrete Fourier transform can beperformed using FFT. From 404, method 400 proceeds to 406.

At 408, the next m is computed. In this step, h is fixed; therefore, mcan be solved using another sub energy optimization function describedas the following:

$\begin{matrix}{{\arg \{ \min_{m} \}} = {\sum_{x = 1}^{k}( {( {{d(x)} - {m(x)}} )^{2} + {\beta \cdot {\sum_{i = 1}^{3}( {{h_{i}(x)} - \frac{\partial{m(x)}}{\partial x_{i}}} )^{2}}}} }} & (13)\end{matrix}$

According to Parseval's theorem, the energy in the time domain is equalto the energy in the frequency domain. Therefore, a Fourier transformcan be applied to equation 10 to yield an object function in thefrequency domain as described below:

arg{min_(M)}=Σ_(x=1) ^(k)((D−M)²+β·Σ_(i=1) ³(H _(i) −W _(i) ^(T)·M)²)  (14)

where D, M, {H_(i)} represents the n-dim discrete Fourier transform ofinput data d, smoothed data m and auxiliary variables {h_(i)}, the inputW_(i) represents the 3D discrete Fourier transform of partial derivativeoperation along i-th dimension, W_(i) ^(T) is the conjugation of W_(i).

This problem has a close form solution described below:

$\begin{matrix}{M = \frac{D + {\beta \cdot {\sum_{i = 1}^{3}( {W_{i}^{T} \cdot H_{i}} )}}}{1 + {\beta \cdot {\sum_{i = 1}^{3}( {W_{i}^{T} \cdot W_{i}} )}}}} & (15)\end{matrix}$

From 408, method 400 proceeds to 410, where an iterative condition ischecked to determine whether the iterative condition has been met. Asdiscussed above, the iterative condition can include a maximum number ofiterations, a maximum number of β, a smoothing quality of the outputdata, or a combination of both. For example, the maximum number ofiterations can be set to 5, or 8-10; the iteration can be determined ifthe number of iterations is equal to the maximum number of iterations.In some cases, the number of iterations affects the flatness betweenrock interfaces. For example, more iterations can result more flatnessbetween rock interfaces. In some cases, the smoothing quality can bedetermined by empirical trial and testing. In some cases, the objectivefunction may converge when β becomes large. In some cases, the smoothedoutput of each iteration may be examined to determine whether theresults converges. In one example, the smoothed output does not changemuch after 10 iterations, and therefore 10 iterations may correspond toa predetermined smoothing quality. In some cases, the number ofiterations may increase if the smoothing quality of the output is notsatisfactory.

If the iterative condition is not met, method 400 proceeds from 410 to412, where the beta value is increased. In some cases, the beta valuecan double in each iteration. From 412, method 400 proceeds to 404,where the next h is computed. If the iterative condition is met, method400 proceeds from 410 to 420.

At 420, the final output data m(x) is calculated by the inverse discreteFourier transform of M. The inverse discrete Fourier transform can beperformed using inverse FFT (IFFT).

FIG. 5 is a high level architecture block diagram of a geophysical dataprocessing system 500 according to an implementation. At a high level,the illustrated system 500 includes a geological interpreter 570 that iscommunicably coupled with a geophysical data processing computer 502through a network 530. The described illustration is only one possibleimplementation of the described subject matter and is not intended tolimit the disclosure to the single described implementation. Those ofordinary skill in the art will appreciate the fact that the describedcomponents can be connected, combined, and/or used in alternative waysconsistent with this disclosure.

The geological interpreter 570 represents a person, an application, setof applications, software, software modules, hardware, or combinationthereof that can be used to analyze the smoothed geophysical data andbuild reservoir model based on the smoothed data. In some cases, thegeological interpreter 570 can also set the initialization parameters ofthe 3D norm zero optimization process discussed above.

The network 530 facilitates communications between the components of thesystem 500 (e.g., between the geological interpreter 570 and thegeophysical data processing computer 502). In some cases, the geologicalinterpreter 570 can access the geophysical data processing computer 502from a remote network. In these or other cases, the network 530 can be awireless or a wireline network. In some cases, the geologicalinterpreter 570 can access the geophysical data processing computer 502locally. In these or other cases, the network 530 can also be a memorypipe, a hardware connection, or any internal or external communicationpaths between the components.

The geophysical data processing computer 502 includes a computing systemconfigured to process the geophysical data using the 3D norm zerooptimization process. In some cases, the algorithm of the 3D norm zerooptimization process can be implemented in an executable computing code,e.g., C/C++ executable codes. In some cases, the geophysical dataprocessing computer 502 can include a standalone Linux system that runsbatch applications. In some cases, the geophysical data processingcomputer 502 can include mobile or personal computers that havesufficient memory size to process each block of the geophysical data.

The computer 502 may comprise a computer that includes an input device,such as a keypad, keyboard, touch screen, microphone, speech recognitiondevice, other device that can accept user information, and/or an outputdevice that conveys information associated with the operation of thecomputer 502, including digital data, visual and/or audio information,or a GUI.

The computer 502 can serve as a client, network component, a server, adatabase or other persistency, and/or any other component of the system500. In some implementations, one or more components of the computer 502may be configured to operate within a cloud-computing-based environment.

At a high level, the computer 502 is an electronic computing deviceoperable to receive, transmit, process, store, or manage data andinformation associated with the system 500. According to someimplementations, the computer 502 may also include or be communicablycoupled with an application server, e-mail server, web server, cachingserver, streaming data server, business intelligence (BI) server, and/orother server.

The computer 502 can receive requests over network 530 from a clientapplication (e.g., executing on another computer 502) and respond to thereceived requests by processing the said requests in an appropriatesoftware application. In addition, requests may also be sent to thecomputer 502 from internal users (e.g., from a command console or byanother appropriate access method), external or third parties, otherautomated applications, as well as any other appropriate entities,individuals, systems, or computers.

Each of the components of the computer 502 can communicate using asystem bus 503. In some implementations, any and/or all the componentsof the computer 502, both hardware and/or software, may interface witheach other and/or the interface 504 over the system bus 503 using anapplication programming interface (API) 512 and/or a service layer 513.The API 512 may include specifications for routines, data structures,and object classes. The API 512 may be either computerlanguage-independent or -dependent and refer to a complete interface, asingle function, or even a set of APIs. The service layer 513 providessoftware services to the computer 502 and/or the system 500. Thefunctionality of the computer 502 may be accessible for all serviceconsumers using this service layer. Software services, such as thoseprovided by the service layer 513, provide reusable, defined businessfunctionalities through a defined interface. For example, the interfacemay be software written in JAVA, C++, or other suitable languageproviding data in Extensible Markup Language (XML) format or othersuitable format. While illustrated as an integrated component of thecomputer 502, alternative implementations may illustrate the API 512and/or the service layer 513 as stand-alone components in relation toother components of the computer 502 and/or system 500. Moreover, any orall parts of the API 512 and/or the service layer 513 may be implementedas child or sub-modules of another software module, enterpriseapplication, or hardware module without departing from the scope of thisdisclosure.

The computer 502 includes an interface 504. Although illustrated as asingle interface 504 in FIG. 5, two or more interfaces 504 may be usedaccording to particular needs, desires, or particular implementations ofthe computer 502 and/or system 500. The interface 504 is used by thecomputer 502 for communicating with other systems in a distributedenvironment—including within the system 500—connected to the network 530(whether illustrated or not). Generally, the interface 504 compriseslogic encoded in software and/or hardware in a suitable combination andoperable to communicate with the network 530. More specifically, theinterface 504 may comprise software supporting one or more communicationprotocols associated with communications such that the network 530 orinterface's hardware is operable to communicate physical signals withinand outside of the illustrated system 500.

The computer 502 includes a processor 505. Although illustrated as asingle processor 505 in FIG. 5, two or more processors may be usedaccording to particular needs, desires, or particular implementations ofthe computer 502 and/or the system 500. Generally, the processor 505executes instructions and manipulates data to perform the operations ofthe computer 502. Specifically, the processor 505 executes thefunctionality required for processing geophysical data.

The computer 502 also includes a memory 506 that holds data for thecomputer 502 and/or other components of the system 500. Althoughillustrated as a single memory 506 in FIG. 5, two or more memories maybe used according to particular needs, desires, or particularimplementations of the computer 502 and/or the system 500. While memory506 is illustrated as an integral component of the computer 502, inalternative implementations, memory 506 can be external to the computer502 and/or the system 500.

The application 507 is an algorithmic software engine providingfunctionality according to particular needs, desires, or particularimplementations of the computer 502 and/or the system 500, particularlywith respect to functionality required for processing geophysical data.For example, application 507 can serve as one or morecomponents/applications described in FIGS. 1-4 and 6-11. Further,although illustrated as a single application 507, the application 507may be implemented as multiple applications 507 on the computer 502. Inaddition, although illustrated as integral to the computer 502, inalternative implementations, the application 507 can be external to thecomputer 502 and/or the system 500.

There may be any number of computers 502 associated with, or externalto, the system 500 and communicating over network 530. Further, theterms “client,” “user,” and other appropriate terminology may be usedinterchangeably as appropriate without departing from the scope of thisdisclosure. Moreover, this disclosure contemplates that many users mayuse one computer 502, or that one user may use multiple computers 502.

FIGS. 6A & 6B are example screenshots 600 a & 600 b, respectively, whichillustrate velocity data according to an implementation. Screenshot 600a (in FIG. 6A) includes raw velocity data 610 and screenshot 600 b (inFIG. 6B) includes smoothed velocity data 620. The velocity data 610 and620 show a complex velocity model with changing contrast and boundary.As illustrated, the smoothed velocity data 620 in FIG. 6B that isproduced by the norm zero smoothing process removes small anomalies,keeps major boundary (edge preserve) while enhancing the boundaryvariations (gradual change of boundary). Although screenshots 600 a and600 b of FIGS. 6A and 6B, respectively, are illustrated in grayscale, inother implementations, the screenshots 600 a and 600 b can display theappropriate velocity data 610 and 620 in various layers of color, suchas red, orange, yellow, green, blue, indigo, violet, and the like, andthe like to help clearly distinguish different data layers.

FIGS. 7A & 7B are example screenshots 700 a & 700 b, respectively, whichillustrate an inline section view of a 3D seismic survey according to animplementation. Screenshot 700 a includes a raw data view 710 andScreenshot 700 b includes a smoothed data view 720. The views 710 and720 represent recorded reflection seismic curves. As illustrated in FIG.7B, after norm zero optimization, the major reflection layers are keptbut the small events between layers have been smoothed out. Therefore,in some cases, the norm-zero optimization process may improve sparse andlayered data. However, the process may not be suitable to preserve smallvariations such as inter-bed reflections or thin layers.

FIGS. 8A & 8B are example screenshots 800 a & 800 b, respectively, whichillustrate a 3D volume view of an acoustic impedance model according toan implementation. Screenshot 800 a includes an impedance model 810obtained based on raw data and screenshot 800 b includes an impedancemodel 820 obtained based on data smoothed by 3D norm zero optimization.A zone 812 a in FIG. 8A displays rough layers and defined edges. Theoptimization parameters include a cut off ratio of 80%, 5 iterations,and a beta value of 0.5. As illustrated in FIG. 8B, after 3D norm zerosmoothing, the layers of zone 812 b are smooth and changes betweenlayers are gradual with better continuation and clarity. Therefore, the3D norm zero smoothing improves the event continuities while preservingedges and suppressing the undesired non-major events. In someimplementations, the impedance model 810 and 820 can be displayed invarious colors, such as red, orange, yellow, green, blue, indigo, violetand the like, based on impedance data, to help clearly distinguishdifferent data layers. For example, impedance data around a value of10000 can be displayed in indigo/violet while impedance data of around avalue of 18000 can be in red. The zone 812 a in FIG. 8A can be displayedin yellow to indicate impedance data of values between about 14000 and16000.

FIGS. 9A & 9B are example screenshots 900 a & 900 b, respectively, whichillustrate a 2D section view of an acoustic impedance model according toan implementation. The screenshot 900 a includes a vertical directionalview of the impedance model 910 obtained based on raw data andscreenshot 900 b includes a vertical directional view of the impedancemodel 920 obtained based on data smoothed by 3D norm zero optimization.Both views show the inline direction at one of the sublines. Asillustrated, the 3D norm zero smoothing suppresses low amplitude imagesand provides better lateral variation layers. In some implementations,the impedance model 910 and 920 can be displayed in various colors, suchas red, orange, yellow, green, blue, indigo, violet, and the like, basedon impedance data, to help clearly distinguish different data layers.For example, impedance data of around a value of 10000 can be displayedin indigo/violet while impedance data of around a value of 18000 can bein red.

FIGS. 10A & 10B are example screenshots 1000 a & 1000 b, respectively,which illustrate a time slice view of an acoustic impedance modelaccording to an implementation. The screenshot 1000 a includes a timeslice view of the impedance model 1010 obtained based on data smoothedby JASON software and screenshot 1000 b includes a time slice view ofthe impedance model 1020 obtained based on data smoothed by 3D norm zerooptimization. Both time slice views represent 444 MS. As illustrated,the 3D norm zero smoothing provides more natural varied changes thatdescribe the subsurface geological information. In some implementations,the impedance model 1010 and 1020 can be displayed in various colors,such as red, orange, yellow, green, blue, indigo, violet, and the like,based on impedance data, to help clearly distinguish different datalayers. For example, impedance data of around a value of 10000 can bedisplayed in indigo/violet while impedance data of around a value of18000 can be in red.

FIGS. 11A & 11B are example screenshots 1100 a & 1100 b, respectively,which illustrate a porosity model according to an implementation. Insome cases, geological interpretation can concentrate on a range ofhorizons where major geological layers (events) are present. In these orother cases, porosity can be computed from geophysical data of theinterest zone to analyze the hydrocarbon mobility. The illustratedporosity model 1110 in FIG. 11A represents a zone of subline (110˜696),cross line (302˜1193), and time (0.5˜1.2 second) of a porosity modelthat is obtained by using support vector machine inversion out of a suitof seismic attributes in Saudi Arabia; and the porosity model 1120 inFIG. 11B is obtained based on the same inversion techniques usingsmoothed data. As illustrated, the porosity model 1120 is moreconsistent, and both the vertical and horizon gradient change becomessmall and continuous compared to the model 1110. In someimplementations, the screenshot 1100 a and 1100 b can display theporosity model 1110 and 1120 in various colors, such as red, orange,yellow, green, blue, indigo, violet, and the like to help clearlydistinguish different data layers.

Implementations of the subject matter and the functional operationsdescribed in this specification can be implemented in digital electroniccircuitry, in tangibly embodied computer software or firmware, incomputer hardware, including the structures disclosed in thisspecification and their structural equivalents, or in combinations ofone or more of them. Implementations of the subject matter described inthis specification can be implemented as one or more computer programs,i.e., one or more modules of computer program instructions encoded on atangible, non-transitory computer-storage medium for execution by, or tocontrol the operation of, data processing apparatus. Alternatively or inaddition, the program instructions can be encoded on an artificiallygenerated propagated signal, e.g., a machine-generated electrical,optical, or electromagnetic signal that is generated to encodeinformation for transmission to suitable receiver apparatus forexecution by a data processing apparatus. The computer-storage mediumcan be a machine-readable storage device, a machine-readable storagesubstrate, a random or serial access memory device, or a combination ofone or more of them.

The terms “data processing apparatus,” “computer,” or “electroniccomputer device” (or equivalent as understood by one of ordinary skillin the art) refer to data processing hardware and encompass all kinds ofapparatus, devices, and machines for processing data, including by wayof example, a programmable processor, a computer, or multiple processorsor computers. The apparatus can also be or further include specialpurpose logic circuitry, e.g., a central processing unit (CPU), an FPGA(field programmable gate array), or an ASIC (application-specificintegrated circuit). In some implementations, the data processingapparatus and/or special purpose logic circuitry may be hardware-basedand/or software-based. The apparatus can optionally include code thatcreates an execution environment for computer programs, e.g., code thatconstitutes processor firmware, a protocol stack, a database managementsystem, an operating system, or a combination of one or more of them.The present disclosure contemplates the use of data processingapparatuses with or without conventional operating systems, for exampleLINUX, UNIX, WINDOWS, MAC OS, ANDROID, IOS or any other suitableconventional operating system.

A computer program, which may also be referred to or described as aprogram, software, a software application, a module, a software module,a script, or code, can be written in any form of programming language,including compiled or interpreted languages, or declarative orprocedural languages, and it can be deployed in any form, including as astand-alone program or as a module, component, subroutine, or other unitsuitable for use in a computing environment. A computer program may, butneed not, correspond to a file in a file system. A program can be storedin a portion of a file that holds other programs or data, e.g., one ormore scripts stored in a markup language document, in a single filededicated to the program in question, or in multiple coordinated files,e.g., files that store one or more modules, sub-programs, or portions ofcode. A computer program can be deployed to be executed on one computeror on multiple computers that are located at one site or distributedacross multiple sites and interconnected by a communication network.While portions of the programs illustrated in the various figures areshown as individual modules that implement the various features andfunctionality through various objects, methods, or other processes, theprograms may instead include a number of sub-modules, third-partyservices, components, libraries, and such, as appropriate. Conversely,the features and functionality of various components can be combinedinto single components as appropriate.

The processes and logic flows described in this specification can beperformed by one or more programmable computers executing one or morecomputer programs to perform functions by operating on input data andgenerating output. The processes and logic flows can also be performedby, and apparatus can also be implemented as, special purpose logiccircuitry, e.g., a CPU, an FPGA, or an ASIC.

Computers suitable for the execution of a computer program can be basedon general or special purpose microprocessors, both, or any other kindof CPU. Generally, a CPU will receive instructions and data from aread-only memory (ROM) or a random access memory (RAM) or both. Theessential elements of a computer are a CPU for performing or executinginstructions and one or more memory devices for storing instructions anddata. Generally, a computer will also include, or be operatively coupledto, receive data from or transfer data to, or both, one or more massstorage devices for storing data, e.g., magnetic, magneto-optical disks,or optical disks. However, a computer need not have such devices.Moreover, a computer can be embedded in another device, e.g., a mobiletelephone, a personal digital assistant (PDA), a mobile audio or videoplayer, a game console, a global positioning system (GPS) receiver, or aportable storage device, e.g., a universal serial bus (USB) flash drive,to name just a few.

Computer-readable media (transitory or non-transitory, as appropriate)suitable for storing computer program instructions and data include allforms of non-volatile memory, media and memory devices, including by wayof example semiconductor memory devices, e.g., erasable programmableread-only memory (EPROM), electrically erasable programmable read-onlymemory (EEPROM), and flash memory devices; magnetic disks, e.g.,internal hard disks or removable disks; magneto-optical disks; andCD-ROM, DVD+/−R, DVD-RAM, and DVD-ROM disks. The memory may storevarious objects or data, including caches, classes, frameworks,applications, backup data, jobs, web pages, web page templates, databasetables, repositories storing business and/or dynamic information, andany other appropriate information including any parameters, variables,algorithms, instructions, rules, constraints, or references thereto.Additionally, the memory may include any other appropriate data, such aslogs, policies, security or access data, reporting files, as well asothers. The processor and the memory can be supplemented by, orincorporated in, special purpose logic circuitry.

To provide for interaction with a user, implementations of the subjectmatter described in this specification can be implemented on a computerhaving a display device, e.g., a CRT (cathode ray tube), LCD (liquidcrystal display), LED (Light Emitting Diode), or plasma monitor, fordisplaying information to the user and a keyboard and a pointing device,e.g., a mouse, trackball, or trackpad by which the user can provideinput to the computer. Input may also be provided to the computer usinga touchscreen, such as a tablet computer surface with pressuresensitivity, a multi-touch screen using capacitive or electric sensing,or other type of touchscreen. Other kinds of devices can be used toprovide for interaction with a user as well; for example, feedbackprovided to the user can be any form of sensory feedback, e.g., visualfeedback, auditory feedback, or tactile feedback; and input from theuser can be received in any form, including acoustic, speech, or tactileinput. In addition, a computer can interact with a user by sendingdocuments to and receiving documents from a device that is used by theuser; for example, by sending web pages to a web browser on a user'sclient device in response to requests received from the web browser.

The term “graphical user interface,” or “GUI,” may be used in thesingular or the plural to describe one or more graphical user interfacesand each of the displays of a particular graphical user interface.Therefore, a GUI may represent any graphical user interface, includingbut not limited to, a web browser, a touch screen, or a command lineinterface (CLI) that processes information and efficiently presents theinformation results to the user. In general, a GUI may include aplurality of user interface (UI) elements, some or all associated with aweb browser, such as interactive fields, pull-down lists, and buttonsoperable by the business suite user. These and other UI elements may berelated to or represent the functions of the web browser.

Implementations of the subject matter described in this specificationcan be implemented in a computing system that includes a back-endcomponent, e.g., as a data server, or that includes a middlewarecomponent, e.g., an application server, or that includes a front-endcomponent, e.g., a client computer having a graphical user interface ora Web browser through which a user can interact with an implementationof the subject matter described in this specification, or anycombination of one or more such back-end, middleware, or front-endcomponents. The components of the system can be interconnected by anyform or medium of wireline and/or wireless digital data communication,e.g., a communication network. Examples of communication networksinclude a local area network (LAN), a radio access network (RAN), ametropolitan area network (MAN), a wide area network (WAN), WorldwideInteroperability for Microwave Access (WIMAX), a wireless local areanetwork (WLAN) using, for example, 802.11 a/b/g/n and/or 802.20, all ora portion of the Internet, and/or any other communication system orsystems at one or more locations. The network may communicate with, forexample, Internet Protocol (IP) packets, Frame Relay frames,Asynchronous Transfer Mode (ATM) cells, voice, video, data, and/or othersuitable information between network addresses.

The computing system can include clients and servers. A client andserver are generally remote from each other and typically interactthrough a communication network. The relationship of client and serverarises by virtue of computer programs running on the respectivecomputers and having a client-server relationship to each other.

In some implementations, any or all of the components of the computingsystem, both hardware and/or software, may interface with each otherand/or the interface using an application programming interface (API)and/or a service layer. The API may include specifications for routines,data structures, and object classes. The API may be either computerlanguage independent or dependent and refer to a complete interface, asingle function, or even a set of APIs. The service layer providessoftware services to the computing system. The functionality of thevarious components of the computing system may be accessible for allservice consumers via this service layer. Software services providereusable, defined business functionalities through a defined interface.For example, the interface may be software written in JAVA, C++, orother suitable language providing data in extensible markup language(XML) format or other suitable format. The API and/or service layer maybe an integral and/or a stand-alone component in relation to othercomponents of the computing system. Moreover, any or all parts of theservice layer may be implemented as child or sub-modules of anothersoftware module, enterprise application, or hardware module withoutdeparting from the scope of this disclosure.

While this specification contains many specific implementation details,these should not be construed as limitations on the scope of anyinvention or on the scope of what may be claimed, but rather asdescriptions of features that may be specific to particularimplementations of particular inventions. Certain features that aredescribed in this specification in the context of separateimplementations can also be implemented in combination in a singleimplementation. Conversely, various features that are described in thecontext of a single implementation can also be implemented in multipleimplementations separately or in any suitable sub-combination. Moreover,although features may be described above as acting in certaincombinations and even initially claimed as such, one or more featuresfrom a claimed combination can in some cases be excised from thecombination, and the claimed combination may be directed to asub-combination or variation of a sub-combination.

Particular implementations of the subject matter have been described.Other implementations, alterations, and permutations of the describedimplementations are within the scope of the following claims as will beapparent to those skilled in the art. While operations are depicted inthe drawings or claims in a particular order, this should not beunderstood as requiring that such operations be performed in theparticular order shown or in sequential order, or that all illustratedoperations be performed (some operations may be considered optional), toachieve desirable results. In certain circumstances, multitasking andparallel processing may be advantageous.

Moreover, the separation and/or integration of various system modulesand components in the implementations described above should not beunderstood as requiring such separation and/or integration in allimplementations, and it should be understood that the described programcomponents and systems can generally be integrated together in a singlesoftware product or packaged into multiple software products.

Accordingly, the above description of example implementations does notdefine or constrain this disclosure. Other changes, substitutions, andalterations are also possible without departing from the spirit andscope of this disclosure.

What is claimed is:
 1. A method, comprising: obtaining a set of rawgeophysical data, wherein the raw geophysical data include 3-dimensional(3D) coordinates; grouping, by a data processing apparatus, the set ofthe raw geophysical data into a plurality of subsets; and processing, bythe data processing apparatus, each subset of the raw geophysical datausing a 3D norm zero objective energy function to generate a subset ofsmoothed geophysical data, wherein the smoothed geophysical data is usedto build a subsurface model.
 2. The method of claim 1, wherein the rawgeophysical data is at least one of impedance data, velocity data, orporosity data.
 3. The method of claim 1, wherein grouping the set of theraw geophysical data into a plurality of subsets comprises: determininggeometry information for the set of the raw geophysical data;determining a memory size for processing a subset of the raw geophysicaldata by the data processing apparatus; and grouping the set of thegeophysical data based on the geometry information and the memory size.4. The method of claim 3, wherein the geometry information includes across line direction of the raw geophysical data.
 5. The method of claim1, wherein the 3D norm zero objective energy function is${{obj} = {\sum_{x = 1}^{k}( {( {{d(x)} - {m(x)}} )^{2} + {\lambda \cdot {\sum_{i = 1}^{3}{C( {\frac{\partial{m(x)}}{\partial x_{i}} \neq 0} )}}}} )}},$where d(x) represents the subset of the raw geophysical data, krepresents the number of the raw geophysical data in the subset, irepresents the dimension of the raw geophysical data, m(x) representsthe subset of the smoothed geophysical data, C( . . . ) represents acounting function, and λ represents a constant weight.
 6. The method ofclaim 1, wherein processing each subset of the raw geophysical datacomprises iteratively processing until an iterative condition is met,the iterative processing comprising: computing an auxiliary value bysolving a first sub energy function, wherein the first sub energyfunction is derived from the 3D norm zero objective energy function witha fixed value of an input data; computing a next input data by solving asecond sub energy function, wherein the second sub energy function isderived from the 3D norm zero objective energy function with a fixedauxiliary value; and increasing a beta value that is included in thefirst and the second sub energy functions.
 7. The method of claim 6,wherein the iteration condition includes at least one of reaching apredetermined number of iterations or a beta value being over apredetermined threshold.
 8. A system, comprising: a memory; and at leastone hardware processor interoperably coupled with the memory andconfigured to: obtain a set of raw geophysical data, wherein the rawgeophysical data include 3-Dimensional (3D) coordinates; group, by adata processing apparatus, the set of the raw geophysical data into aplurality of subsets; and process, by the data processing apparatus,each subset of the raw geophysical data using a 3D norm zero objectiveenergy function to generate a subset of smoothed geophysical data,wherein the smoothed geophysical data is used to build a subsurfacemodel.
 9. The system of claim 8, wherein the raw geophysical data is atleast one of impedance data, velocity data, or porosity data.
 10. Thesystem of claim 8, wherein grouping the set of the raw geophysical datainto a plurality of subsets comprises: determining geometry informationfor the set of the raw geophysical data; determining a memory size forprocessing a subset of the raw geophysical data by the data processingapparatus; and grouping the set of the geophysical data based on thegeometry information and the memory size.
 11. The system of claim 10,wherein the geometry information includes a cross line direction of theraw geophysical data.
 12. The system of claim 8, wherein the 3D normzero objective energy function is${{obj} = {\sum_{x = 1}^{k}( {( {{d(x)} - {m(x)}} )^{2} + {\lambda \cdot {\sum_{i = 1}^{3}{C( {\frac{\partial{m(x)}}{\partial x_{i}} \neq 0} )}}}} )}},$where d(x) represents the subset of the raw geophysical data, krepresents the number of the raw geophysical data in the subset, irepresents the dimension of the raw geophysical data, m(x) representsthe subset of the smoothed geophysical data, C( . . . ) represents acounting function, and λ represents a constant weight.
 13. The system ofclaim 8, wherein processing each subset of the raw geophysical datacomprises iteratively processing until an iterative condition is met,the iterative processing comprising: computing an auxiliary value bysolving a first sub energy function, wherein the first sub energyfunction is derived from the 3D norm zero objective energy function witha fixed value of an input data; computing a next input data by solving asecond sub energy function, wherein the second sub energy function isderived from the 3D norm zero objective energy function with a fixedauxiliary value; and increasing a beta value that is included in thefirst and the second sub energy functions.
 14. The system of claim 13,wherein the iteration condition includes at least one of reaching apredetermined number of iterations or a beta value being over apredetermined threshold.
 15. A non-transitory, computer-readable mediumstoring computer-readable instructions, the instructions executable by acomputer and configured to: obtain a set of raw geophysical data,wherein the raw geophysical data include 3-Dimensional (3D) coordinates;group, by a data processing apparatus, the set of the raw geophysicaldata into a plurality of subsets; and process, by the data processingapparatus, each subset of the raw geophysical data using a 3D norm zeroobjective energy function to generate a subset of smoothed geophysicaldata, wherein the smoothed geophysical data is used to build asubsurface model.
 16. The medium of claim 15, wherein the rawgeophysical data is at least one of impedance data, velocity data, orporosity data.
 17. The medium of claim 15, wherein grouping the set ofthe raw geophysical data into a plurality of subsets comprises:determining geometry information for the set of the raw geophysicaldata; determining a memory size for processing a subset of the rawgeophysical data by the data processing apparatus; and grouping the setof the geophysical data based on the geometry information and the memorysize.
 18. The medium of claim 17, wherein the geometry informationincludes a cross line direction of the raw geophysical data.
 19. Themedium of claim 15, wherein the 3D norm zero objective energy functionis${{obj} = {\sum_{x = 1}^{k}( {( {{d(x)} - {m(x)}} )^{2} + {\lambda \cdot {\sum_{i = 1}^{3}{C( {\frac{\partial{m(x)}}{\partial x_{i}} \neq 0} )}}}} )}},$where d(x) represents the subset of the raw geophysical data, krepresents the number of the raw geophysical data in the subset, irepresents the dimension of the raw geophysical data, m(x) representsthe subset of the smoothed geophysical data, C( . . . ) represents acounting function, and λ represents a constant weight.
 20. The medium ofclaim 15, wherein processing each subset of the raw geophysical datacomprises iteratively processing until an iterative condition is met,wherein the iteration condition includes at least one of reaching apredetermined number of iterations or a beta value being over apredetermined threshold, and wherein the iterative processing includes:computing an auxiliary value by solving a first sub energy function,wherein the first sub energy function is derived from the 3D norm zeroobjective energy function with a fixed value of an input data; computinga next input data by solving a second sub energy function, wherein thesecond sub energy function is derived from the 3D norm zero objectiveenergy function with a fixed auxiliary value; and increasing a betavalue that is included in the first and the second sub energy functions.